We investigated the transmission of the long-period fiber grating (LPFG) with the linear chirp and with the nonlinear citric chirp, and detailed the cross-coupled constant Kac and chirp f, which affect the LPFG's transmission. With various cross-coupled constants, the filter can be of band-pass, band- reject or partial band-passing/reject. The effects of the high order citric chirp on the long-period fiber grating were in transmission and in the shift of the center wavelength.